The Vans challenge is a viral internet challenge that began in March 2019 where people show their Vans shoes landing right-side up after tossing them in the air. The viral sensation reportedly started after a Twitter user shared a video of the occurrence, which was captioned: “Did you know it doesn’t matter how you throw your Vans they will land facing up.” Since then, multiple people on social media posted similar videos of them throwing their Vans in the air and landing right-side up, along with Crocs, UGG boots, and other popular shoes. This theory proved false, as these shoes have not always landed facing up after tossing them.
Automated Lip Reading
Automated Lip Reading (ALR) is a software technology developed by speech recognition expert Frank Hubner. A video image of a person talking can be analysed by the software. The shapes made by the lips can be examined and then turned into sounds. The sounds are compared to a dictionary to create matches to the words being spoken. The technology was used successfully to analyse silent home movie footage of Adolf Hitler taken by Eva Braun at their Bavarian retreat Berghof. The video, with words, was included in a documentary titled "Hitler's Private World", Revealed Studios, 2006 Source: New Technology catches Hitler off guard
Belief–desire–intention software model
The belief–desire–intention software model (BDI) is a software model developed for programming intelligent agents. Superficially characterized by the implementation of an agent's beliefs, desires and intentions, it actually uses these concepts to solve a particular problem in agent programming. In essence, it provides a mechanism for separating the activity of selecting a plan (from a plan library or an external planner application) from the execution of currently active plans. Consequently, BDI agents are able to balance the time spent on deliberating about plans (choosing what to do) and executing those plans (doing it). A third activity, creating the plans in the first place (planning), is not within the scope of the model, and is left to the system designer and programmer. == Overview == In order to achieve this separation, the BDI software model implements the principal aspects of Michael Bratman's theory of human practical reasoning (also referred to as Belief-Desire-Intention, or BDI). That is to say, it implements the notions of belief, desire and (in particular) intention, in a manner inspired by Bratman. For Bratman, desire and intention are both pro-attitudes (mental attitudes concerned with action). He identifies commitment as the distinguishing factor between desire and intention, noting that it leads to (1) temporal persistence in plans and (2) further plans being made on the basis of those to which it is already committed. The BDI software model partially addresses these issues. Temporal persistence, in the sense of explicit reference to time, is not explored. The hierarchical nature of plans is more easily implemented: a plan consists of a number of steps, some of which may invoke other plans. The hierarchical definition of plans itself implies a kind of temporal persistence, since the overarching plan remains in effect while subsidiary plans are being executed. An important aspect of the BDI software model (in terms of its research relevance) is the existence of logical models through which it is possible to define and reason about BDI agents. Research in this area has led, for example, to the axiomatization of some BDI implementations, as well as to formal logical descriptions such as Anand Rao and Michael Georgeff's BDICTL. The latter combines a multiple-modal logic (with modalities representing beliefs, desires and intentions) with the temporal logic CTL. More recently, Michael Wooldridge has extended BDICTL to define LORA (the Logic Of Rational Agents), by incorporating an action logic. In principle, LORA allows reasoning not only about individual agents, but also about communication and other interaction in a multi-agent system. The BDI software model is closely associated with intelligent agents, but does not, of itself, ensure all the characteristics associated with such agents. For example, it allows agents to have private beliefs, but does not force them to be private. It also has nothing to say about agent communication. Ultimately, the BDI software model is an attempt to solve a problem that has more to do with plans and planning (the choice and execution thereof) than it has to do with the programming of intelligent agents. This approach has recently been proposed by Steven Umbrello and Roman Yampolskiy as a means of designing autonomous vehicles for human values. == BDI agents == A BDI agent is a particular type of bounded rational software agent, imbued with particular mental attitudes, viz: Beliefs, Desires and Intentions (BDI). === Architecture === This section defines the idealized architectural components of a BDI system. Beliefs: Beliefs represent the informational state of the agent–its beliefs about the world (including itself and other agents). Beliefs can also include inference rules, allowing forward chaining to lead to new beliefs. Using the term belief rather than knowledge recognizes that what an agent believes may not necessarily be true (and in fact may change in the future). Beliefset: Beliefs are stored in database (sometimes called a belief base or a belief set), although that is an implementation decision. Desires: Desires represent the motivational state of the agent. They represent objectives or situations that the agent would like to accomplish or bring about. Examples of desires might be: find the best price, go to the party or become rich. Goals: A goal is a desire that has been adopted for active pursuit by the agent. Usage of the term goals adds the further restriction that the set of active desires must be consistent. For example, one should not have concurrent goals to go to a party and to stay at home – even though they could both be desirable. Intentions: Intentions represent the deliberative state of the agent – what the agent has chosen to do. Intentions are desires to which the agent has to some extent committed. In implemented systems, this means the agent has begun executing a plan. Plans: Plans are sequences of actions (recipes or knowledge areas) that an agent can perform to achieve one or more of its intentions. Plans may include other plans: my plan to go for a drive may include a plan to find my car keys. This reflects that in Bratman's model, plans are initially only partially conceived, with details being filled in as they progress. Events: These are triggers for reactive activity by the agent. An event may update beliefs, trigger plans or modify goals. Events may be generated externally and received by sensors or integrated systems. Additionally, events may be generated internally to trigger decoupled updates or plans of activity. BDI was also extended with an obligations component, giving rise to the BOID agent architecture to incorporate obligations, norms and commitments of agents that act within a social environment. === BDI interpreter === This section defines an idealized BDI interpreter that provides the basis of SRI's PRS lineage of BDI systems: initialize-state repeat options: option-generator (event-queue) selected-options: deliberate(options) update-intentions(selected-options) execute() get-new-external-events() drop-unsuccessful-attitudes() drop-impossible-attitudes() end repeat === Limitations and criticisms === The BDI software model is one example of a reasoning architecture for a single rational agent, and one concern in a broader multi-agent system. This section bounds the scope of concerns for the BDI software model, highlighting known limitations of the architecture. Learning: BDI agents lack any specific mechanisms within the architecture to learn from past behavior and adapt to new situations. Three attitudes: Classical decision theorists and planning research questions the necessity of having all three attitudes, distributed AI research questions whether the three attitudes are sufficient. Logics: The multi-modal logics that underlie BDI (that do not have complete axiomatizations and are not efficiently computable) have little relevance in practice. Multiple agents: In addition to not explicitly supporting learning, the framework may not be appropriate to learning behavior. Further, the BDI model does not explicitly describe mechanisms for interaction with other agents and integration into a multi-agent system. Explicit goals: Most BDI implementations do not have an explicit representation of goals. Lookahead: The architecture does not have (by design) any lookahead deliberation or forward planning. This may not be desirable because adopted plans may use up limited resources, actions may not be reversible, task execution may take longer than forward planning, and actions may have undesirable side effects if unsuccessful. == BDI agent implementations == === 'Pure' BDI === Procedural Reasoning System (PRS) IRMA (not implemented but can be considered as PRS with non-reconsideration) UM-PRS OpenPRS Distributed Multi-Agent Reasoning System (dMARS) AgentSpeak(L) – see Jason below AgentSpeak(RT) Agent Real-Time System (ARTS) (ARTS) JAM JACK Intelligent Agents JADEX (open source project) JaKtA JASON GORITE SPARK 3APL 2APL GOAL agent programming language CogniTAO (Think-As-One) Living Systems Process Suite PROFETA Gwendolen (Part of the Model Checking Agent Programming Languages Framework) === Extensions and hybrid systems === JACK Teams CogniTAO (Think-As-One) Living Systems Process Suite Brahms JaCaMo
Use of artificial intelligence by the United States Department of Defense
The United States Department of Defense has been analyzing and employing military applications of artificial intelligence since at least 2014. The program initially focused on drones and other robots, but has also been using large language models for military research and analysis. The current US policy on lethal autonomous weapons is Department of Defense Directive 3000.09, updated in January 2023. == Background == The United States Department of Defense began developing lethal autonomous weapons as early as the Reagan administration. An early version of the Tomahawk missile could have been used to destroy Soviet ships without direct human control; the initiative was abandoned after the United States and the Soviet Union signed START I. By 2014, the United Kingdom, Israel, and Norway had already begun using missiles equipped with artificial intelligence systems. The Department of Defense established a policy on the use of artificial intelligence in 2012. == History == === 2016–2017: Carter secretaryship === In May 2016, secretary of defense Ash Carter stated that his Third Offset strategy would include utilizing artificial intelligence as a military advantage. The New York Times reported that year that the Department of Defense had tested an autonomous drone at an approximation of a Middle Eastern village at Camp Edwards. Deputy secretary of defense Robert O. Work, who advocated for developing artificial intelligence, told the Times that the United States needed to compete with China and Russia by having a tactical advantage they could not easily replicate. The initiative was developed by DARPA beginning in 2015. The use of artificial intelligence in the U.S. military was controversial within the department; in February, Paul Scharre, who worked for the Office of the Secretary of Defense in the secretaryships of Robert Gates and Leon Panetta, published a report about the risks of artificial intelligence for broad military applications. === 2017–2019: Mattis secretaryship === By 2017, the United States Air Force had already begun using artificial intelligence in military robots. The Air Force's use of Neurala, an artificial intelligence company, concerned officials in the Department of Defense after an investigation found that Neurala had accepted money from an investment firm with funding from a state-run Chinese company. The Department of Defense began heavily investing in artificial intelligence after Work established Project Maven, an initiative to encourage the development and integration of artificial intelligence in the military, in April 2017. In May 2018, secretary of defense Jim Mattis privately expressed to president Donald Trump that he needed to establish a national strategy on artificial intelligence, quoting an article from former secretary of state Henry Kissinger that called for a presidential commission on the technology. The Department of Defense established the Joint Artificial Intelligence Center the following month. Google began working with the Department of Defense on analyzing drone footage as early as March. Google's involvement in the initiative led to protests from employees and mass resignations. Seeking to quell internal unrest, Google stated it would not renew its contract with the Department of Defense in June. The Department of Defense announced an artificial intelligence contract with Microsoft in October. === 2025–present: Hegseth secretaryship === In December 2025, secretary of defense Pete Hegseth announced GenAI.mil, an artificial intelligence platform for the Department of Defense. In a video announcing the platform, Hegseth stated that Department of Defense workers would be able to "conduct deep research, format documents and even analyze video or imagery." The Department of Defense contracted first Gemini by Google, then ChatGPT by OpenAI, and finally Grok by xAI for the platform. Claude by Anthropic was also contracted by the Department of Defense and was in use on secure servers until it was revealed that Claude had been used in the 2026 operation to capture Nicolás Maduro, who was at the time the leader of Venezuela. This revelation sparked a high-profile dispute over Anthropic's ability to constrain Claude's useage, resulting in the termination of Anthropic's $200 million defense contract. The Department of Defense also moved to label Anthropic a supply chain risk, which was later blocked by a federal judge.
Veo (text-to-video model)
Veo, or Google Veo, is a text-to-video model developed by Google DeepMind and announced in May 2024. As a generative AI model, it creates videos based on user prompts. Veo 3, released in May 2025, can also generate accompanying audio. == Development == In May 2024, a multimodal video generation model called Veo was announced at Google I/O 2024. Google claimed that it could generate 1080p videos over a minute long. In December 2024, Google released Veo 2, available via VideoFX. It supports 4K resolution video generation and has an improved understanding of physics. In April 2025, Google announced that Veo 2 became available for advanced users on the Gemini app. In May 2025, Google released Veo 3, which not only generates videos but also creates synchronized audio — including dialogue, sound effects, and ambient noise — to match the visuals. Google also announced Flow, a video-creation tool powered by Veo and Imagen. Google DeepMind CEO Demis Hassabis described the release as the moment when AI video generation left the era of the silent film. This was rebranded as Google Flow at the 2026 Google I/O keynote, along with the announcement of Google Flow Music. == Capabilities == Google Veo can be purchased at multiple subscription tiers and through Google "AI credits". The software itself can be run by two different consoles, Google Gemini and Google Flow. Gemini being geared towards shorter, quicker, and faster projects, using the Gemini AI chat model, with Google Flow, which is essentially a movie editor allowing users to create longer projects with continuity, using the same characters and actors. Users can create a maximum of eight seconds per clip. According to Gizmodo Veo 3 users were directing the model to generate low-quality content, such as man on the street interviews or haul videos of people unboxing products. 404 Media reported that the tool tended to repeat the same joke in response to different prompts. Commentators speculated that Google had trained the service on YouTube videos or Reddit posts. Google itself had not stated the source of its training content. In July 2025, Media Matters for America reported that racist and antisemitic videos generated using Veo 3 were being uploaded to TikTok. Ryan Whitwam of Ars Technica commented, "In a perfect world, Veo 3 would refuse to create these videos, but vagueness in the prompt and the AI's inability to understand the subtleties of racist tropes (i.e., the use of monkeys instead of humans in some videos) make it easy to skirt the rules."
Situated
In artificial intelligence and cognitive science, the term situated refers to an agent which is embedded in an environment. The term situated is commonly used to refer to robots, but some researchers argue that software agents can also be situated if: they exist in a dynamic (rapidly changing) environment, which they can manipulate or change through their actions, and which they can sense or perceive. Examples might include web-based agents, which can alter data or trigger processes (such as purchases) over the internet, or virtual-reality bots which inhabit and change virtual worlds, such as Second Life. Being situated is generally considered to be part of being embodied, but it is useful to consider each perspective individually. The situated perspective emphasizes that intelligent behaviour derives from the environment and the agent's interactions with it. The nature of these interactions are defined by an agent's embodiment.
T-norm
In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary operation used in the framework of probabilistic metric spaces and in multi-valued logic, specifically in fuzzy logic. A t-norm generalizes intersection in a lattice and conjunction in logic. The name triangular norm refers to the fact that in the framework of probabilistic metric spaces t-norms are used to generalize the triangle inequality of ordinary metric spaces. == Definition == A t-norm is a function T: [0, 1] × [0, 1] → [0, 1] that satisfies the following properties: Commutativity: T(a, b) = T(b, a) Monotonicity: T(a, b) ≤ T(c, d) if a ≤ c and b ≤ d Associativity: T(a, T(b, c)) = T(T(a, b), c) The number 1 acts as identity element: T(a, 1) = a Since a t-norm is a binary algebraic operation on the interval [0, 1], infix algebraic notation is also common, with the t-norm usually denoted by ∗ {\displaystyle } . The defining conditions of the t-norm are exactly those of a partially ordered abelian monoid on the real unit interval [0, 1]. (Cf. ordered group.) The monoidal operation of any partially ordered abelian monoid L is therefore by some authors called a triangular norm on L. === Classification of t-norms === A t-norm is called continuous if it is continuous as a function, in the usual interval topology on [0, 1]2. (Similarly for left- and right-continuity.) A t-norm is called strict if it is continuous and strictly monotone. A t-norm is called nilpotent if it is continuous and each x in the open interval (0, 1) is nilpotent, that is, there is a natural number n such that x ∗ {\displaystyle } ... ∗ {\displaystyle } x (n times) equals 0. A t-norm ∗ {\displaystyle } is called Archimedean if it has the Archimedean property, that is, if for each x, y in the open interval (0, 1) there is a natural number n such that x ∗ {\displaystyle } ... ∗ {\displaystyle } x (n times) is less than or equal to y. The usual partial ordering of t-norms is pointwise, that is, T1 ≤ T2 if T1(a, b) ≤ T2(a, b) for all a, b in [0, 1]. As functions, pointwise larger t-norms are sometimes called stronger than those pointwise smaller. In the semantics of t-norm fuzzy logics, however, the larger a t-norm, the weaker (in terms of logical strength) conjunction it represents. == Prominent examples == Minimum t-norm ⊤ m i n ( a , b ) = min { a , b } , {\displaystyle \top _{\mathrm {min} }(a,b)=\min\{a,b\},} also called the Gödel t-norm, as it is the standard semantics for conjunction in Gödel fuzzy logic. Besides that, it occurs in most t-norm based fuzzy logics as the standard semantics for weak conjunction. It is the pointwise largest t-norm (see the properties of t-norms below). Product t-norm ⊤ p r o d ( a , b ) = a ⋅ b {\displaystyle \top _{\mathrm {prod} }(a,b)=a\cdot b} (the ordinary product of real numbers). Besides other uses, the product t-norm is the standard semantics for strong conjunction in product fuzzy logic. It is a strict Archimedean t-norm. Łukasiewicz t-norm ⊤ L u k ( a , b ) = max { 0 , a + b − 1 } . {\displaystyle \top _{\mathrm {Luk} }(a,b)=\max\{0,a+b-1\}.} The name comes from the fact that the t-norm is the standard semantics for strong conjunction in Łukasiewicz fuzzy logic. It is a nilpotent Archimedean t-norm, pointwise smaller than the product t-norm. Drastic t-norm ⊤ D ( a , b ) = { b if a = 1 a if b = 1 0 otherwise. {\displaystyle \top _{\mathrm {D} }(a,b)={\begin{cases}b&{\mbox{if }}a=1\\a&{\mbox{if }}b=1\\0&{\mbox{otherwise.}}\end{cases}}} The name reflects the fact that the drastic t-norm is the pointwise smallest t-norm (see the properties of t-norms below). It is a right-continuous Archimedean t-norm. Nilpotent minimum ⊤ n M ( a , b ) = { min ( a , b ) if a + b > 1 0 otherwise {\displaystyle \top _{\mathrm {nM} }(a,b)={\begin{cases}\min(a,b)&{\mbox{if }}a+b>1\\0&{\mbox{otherwise}}\end{cases}}} is a standard example of a t-norm that is left-continuous, but not continuous. Despite its name, the nilpotent minimum is not a nilpotent t-norm. Hamacher product ⊤ H 0 ( a , b ) = { 0 if a = b = 0 a b a + b − a b otherwise {\displaystyle \top _{\mathrm {H} _{0}}(a,b)={\begin{cases}0&{\mbox{if }}a=b=0\\{\frac {ab}{a+b-ab}}&{\mbox{otherwise}}\end{cases}}} is a strict Archimedean t-norm, and an important representative of the parametric classes of Hamacher t-norms and Schweizer–Sklar t-norms. == Properties of t-norms == The drastic t-norm is the pointwise smallest t-norm and the minimum is the pointwise largest t-norm: ⊤ D ( a , b ) ≤ ⊤ ( a , b ) ≤ ⊤ m i n ( a , b ) , {\displaystyle \top _{\mathrm {D} }(a,b)\leq \top (a,b)\leq \mathrm {\top _{min}} (a,b),} for any t-norm ⊤ {\displaystyle \top } and all a, b in [0, 1]. In particular, we have that: ⊤ D ( a , b ) ≤ ⊤ L u k ( a , b ) ≤ ⊤ p r o d ( a , b ) ≤ ⊤ m i n ( a , b ) , {\displaystyle \top _{\mathrm {D} }(a,b)\leq \top _{\mathrm {Luk} }(a,b)\leq \top _{\mathrm {prod} }(a,b)\leq \mathrm {\top _{min}} (a,b),} for all a, b in [0, 1]. For every t-norm T, the number 0 acts as null element: T(a, 0) = 0 for all a in [0, 1]. A t-norm T has zero divisors if and only if it has nilpotent elements; each nilpotent element of T is also a zero divisor of T. The set of all nilpotent elements is an interval [0, a] or [0, a), for some a in [0, 1]. === Properties of continuous t-norms === Although real functions of two variables can be continuous in each variable without being continuous on [0, 1]2, this is not the case with t-norms: a t-norm T is continuous if and only if it is continuous in one variable, i.e., if and only if the functions fy(x) = T(x, y) are continuous for each y in [0, 1]. Analogous theorems hold for left- and right-continuity of a t-norm. A continuous t-norm is Archimedean if and only if 0 and 1 are its only idempotents. A continuous Archimedean t-norm is strict if 0 is its only nilpotent element; otherwise it is nilpotent. By definition, moreover, a continuous Archimedean t-norm T is nilpotent if and only if each x < 1 is a nilpotent element of T. Thus with a continuous Archimedean t-norm T, either all or none of the elements of (0, 1) are nilpotent. If it is the case that all elements in (0, 1) are nilpotent, then the t-norm is isomorphic to the Łukasiewicz t-norm; i.e., there is a strictly increasing function f such that ⊤ ( x , y ) = f − 1 ( ⊤ L u k ( f ( x ) , f ( y ) ) ) . {\displaystyle \top (x,y)=f^{-1}(\top _{\mathrm {Luk} }(f(x),f(y))).} If on the other hand it is the case that there are no nilpotent elements of T, the t-norm is isomorphic to the product t-norm. In other words, all nilpotent t-norms are isomorphic, the Łukasiewicz t-norm being their prototypical representative; and all strict t-norms are isomorphic, with the product t-norm as their prototypical example. The Łukasiewicz t-norm is itself isomorphic to the product t-norm undercut at 0.25, i.e., to the function p(x, y) = max(0.25, x ⋅ y) on [0.25, 1]2. For each continuous t-norm, the set of its idempotents is a closed subset of [0, 1]. Its complement—the set of all elements that are not idempotent—is therefore a union of countably many non-overlapping open intervals. The restriction of the t-norm to any of these intervals (including its endpoints) is Archimedean, and thus isomorphic either to the Łukasiewicz t-norm or the product t-norm. For such x, y that do not fall into the same open interval of non-idempotents, the t-norm evaluates to the minimum of x and y. These conditions actually give a characterization of continuous t-norms, called the Mostert–Shields theorem, since every continuous t-norm can in this way be decomposed, and the described construction always yields a continuous t-norm. The theorem can also be formulated as follows: A t-norm is continuous if and only if it is isomorphic to an ordinal sum of the minimum, Łukasiewicz, and product t-norm. A similar characterization theorem for non-continuous t-norms is not known (not even for left-continuous ones), only some non-exhaustive methods for the construction of t-norms have been found. == Residuum == For any left-continuous t-norm ⊤ {\displaystyle \top } , there is a unique binary operation ⇒ {\displaystyle \Rightarrow } on [0, 1] such that ⊤ ( z , x ) ≤ y {\displaystyle \top (z,x)\leq y} if and only if z ≤ ( x ⇒ y ) {\displaystyle z\leq (x\Rightarrow y)} for all x, y, z in [0, 1]. This operation is called the residuum of the t-norm. In prefix notation, the residuum of a t-norm ⊤ {\displaystyle \top } is often denoted by ⊤ → {\displaystyle {\vec {\top }}} or by the letter R. The interval [0, 1] equipped with a t-norm and its residuum forms a residuated lattice. The relation between a t-norm T and its residuum R is an instance of adjunction (specifically, a Galois connection): the residuum forms a right adjoint R(x, –) to the functor T(–, x) for each x in the lattice [0, 1] taken as a poset category. In the standard semantics of t-norm based fuzzy logics, where conjunction is interpreted by a t-norm, the residuum plays the role of implication (often